Studies of the Boundary Behaviour of Functions Related to Partial Differential Equations and Several Complex Variables
| Autor: | Persson, Håkan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
uniformly parabolic equations
non-linear parabolic equations linear growth Lipschitz domain NTA-domain Riesz measure boundary behavior boundary Harnack degenerate parabolic parabolic measure plurisubharmonic functions continuous boundary hyperconvexity bounded exhaustion function Hölder for all exponents log-lipschitz boundary regularity approximation Mergelyan type approximation plurisubharmonic functions on compacts Jensen measures monotone convergence plurisubharmonic extension plurisubharmonic boundary values |
| Druh dokumentu: | Doctoral Thesis<br />Text |
| Popis: | This thesis consists of a comprehensive summary and six scientific papers dealing with the boundary behaviour of functions related to parabolic partial differential equations and several complex variables. Paper I concerns solutions to non-linear parabolic equations of linear growth. The main results include a backward Harnack inequality, and the Hölder continuity up to the boundary of quotients of non-negative solutions vanishing on the lateral boundary of an NTA cylinder. It is also shown that the Riesz measure associated with such solutions has the doubling property. Paper II is concerned with solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a weight in the Muckenhoupt class 1+2/n. Two main results are that non-negative solutions which vanish continuously on the lateral boundary of an NTA cylinder satisfy a backward Harnack inequality and that the quotient of two such functions is Hölder continuous up to the boundary. Another result is that the parabolic measure associated to such equations has the doubling property. In Paper III, it is shown that a bounded pseudoconvex domain whose boundary is α-Hölder for each 0 |
| Databáze: | Networked Digital Library of Theses & Dissertations |
| Externí odkaz: |
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